Shelley had it that "poets are the unacknowledged legislators of the world", and that "poetry is the record of the best and happiest moments of the happiest and best minds".

For Jeremy Paxman, though, it is an art form that has "connived at its own irrelevance", as he believes that poets today have stopped talking to the public and are only addressing each other.

Paxman called for an "inquisition" in which "poets [would be] called to account for their poetry", appearing before a panel of the public where they would have to "explain why they chose to write about the particular subject they wrote about, and why they chose the particular form and language, idiom, the rest of it, because it would be a really illuminating experience for everybody".

The television presenter was speaking after judging this year's Forward prize for poetry, one of poetry's most prestigious awards, which has gone in the past to names including Carol Ann Duffy and Ted Hughes.

Naming the contenders for the best collection prize – Colette Bryce, John Burnside, Louise Glück, Kei Miller and Hugo Williams – Paxman said there was a "whole pile of really good poems here", and "nothing on the shortlist that I don't feel better for having read".

But he also expressed the wish that poetry more generally "would raise its game a little bit, raise its sights", and "aim to engage with ordinary people much more".

"I think poetry has really rather connived at its own irrelevance and that shouldn't happen, because it's the most delightful thing," said Paxman. "It seems to me very often that poets now seem to be talking to other poets and that is not talking to people as a whole."

His words come as official figures show a decline in poetry sales. Five years ago, in 2009, sales of poetry stood at £8.4m. By 2013, they had fallen to £7.8m, according to Nielsen BookScan.

Michael Symmons Roberts, a poet who has both won and judged the Forward prize, said that Paxman's proclamation was "not without foundation in terms of the symptoms – it would be stupid for poets to say poetry is as dominant as the novel" – but he disagreed with Paxman's diagnosis.

"Poetry doesn't have the currency in our culture that novels and films have – people who would be embarrassed not to have read the latest Julian Barnes or Martin Amis are not the slightest bit embarrassed not to have read the latest John Burnside or Carol Ann Duffy. But I don't believe it's quite good enough to say this is a problem of poets and poetry – it's far more complex," said Roberts.

Poetry, he said, still had a "powerful role in our culture": poems are still featured on public radio, and read at funerals and weddings.

"We are still a nation which feels it needs and reaches for poetry at key moments; what has been lost is the habit of buying and reading books of poetry," said Roberts. But he said this was not because poets were only writing for each other, as Paxman claims.

"There is an awful lot of very powerful, lyrical, and readable poetry being written today," he said, but what was needed was education, because "we have lost the sense that poetry sits halfway between prose and music – that you can't expect to read it like a novel. We are quite used to downloading an album and listening to certain tracks … poetry needs to be consumed in that way.

"You live with poems, reread them, and they will give more and more riches each time. So it would be true to say that we have forgotten as a nation how to read books of poetry – but we still have a powerful need for it."

Dr Jeremy Noel-Tod, editor of the Oxford Companion to Modern Poetry, said he tended to respond to sentiments like Paxman's by citing Frank O'Hara: "If they don't need poetry, bully for them. I like the movies too".

"Lyric poetry has rarely produced immediately popular art. But the poetry that people need emerges over time. And very often it's by writers considered irrelevant or insufficiently ordinary by the commentators of their day," said Noel-Tod. "Frank O'Hara was once patronised as a niche poet of the New York art scene. Fifty years later, he's being recited by Don Draper on Mad Men and is one of the most influential voices around."

But Susannah Herbert, director of the Forward Arts Foundation, welcomed Paxman's "splendidly provocative proposals for a Forward inquisition", expressing the hope that they would "kick start an overdue national debate about the power of well-chosen words, communication and the role of poetry in our collective lives".

"We'd dearly love to see poets mount a series of counter-inquisitions in their turn, grilling journalists, politicians bureaucrats and all users and abusers of words," said Herbert.

Paxman was one of five judges on the Forward panel, alongside the musician Cerys Matthews and three poets: Dannie Abse, Helen Mort and Vahni Capildeo.

The judges read 170 collections and 254 single poems before arriving at their shortlists, with the £10,000 best collection prize pitting Bryce's poetic account of growing up in Derry during the Troubles, The Whole & Rain-domed Universe, against Burnside's All One Breath – his first collection since his Forward and TS Eliot prize-winning Black Cat Bone.

Glück, a former US poet laureate, is shortlisted for Faithful and Virtuous Night, in which she draws "on the worlds of fairytale, of dream and of waking life", according to her publisher; Jamaican poet Miller for The Cartographer Tries to Map a Way to Zion; and Williams for I Knew the Bride, which includes the poet's recording of his ongoing hospital treatment in the poem From the Dialysis Ward.

Alongside the five poets competing for the £10,000 best collection prize, six are in the running for the £5,000 best first collection award, including former machine gunner and Iraq veteran Kevin Powers, and five for the £1,000 Forward prize for best single poem.

Abse noted that many of the poets making their debut this year were inspired by conflict, whether in Iraq, Sri Lanka or Ireland. "One can see their talent," he said.

William Sieghart, who founded the Forward prizes in 1991, said the writers on the shortlists "bring news that stays news, in fresh and startling language", and that their voices "remind readers that, in an age of shortened attention spans, good poetry can communicate insights and visions with a power other art forms can only envy".

From the skewering of Chloe Smith to the interview where he asked Michael Howard the same question 12 times – via some scorn for the weather – here are the best clips from Paxman's 25 years on the show